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The fence and the main gate of Mr. Mateo's house are to be renovated. He wants at least half of the total height of the fence to be made of concrete materials and the remaining part to be made of metal (steel). For the gate, Mr. Mateo wants it to be made of both wood and metal. Being the most popular architect in your locality, Mr. Mateo contracted you to sketch a design of the fence and gate. He wants you to color your design using three colors only. Your design should also be accompanied by an estimation of labor and material costs, considering the perimeter of the lot and the height of the fence. The lot has sides whose measures are 6√18 m, √98 m, √162 m, and √128 m. The height of both the fence and gate is 2.5 m.